You can use the .NET Framework to implement an external Membership Database and then develop a custom Membership Provider class. You can then override all the methods and implement the required functionality.

Finally you need to configure Umbraco to use it in the web.config file, replacing the default setting for Membership Provider.

Bare in mind Umbraco has two Providers, one for backoffice users and another for website users, so make sure you configure the right one. UsersMembershipProvider is for backoffice.

If you use the standard membership database schema then you should be able to find a standard implementation of the MembershipProvider.

If you use a custom database schema then you will need to override methods in your custom MembershipProvider implementation.

Note: You must implement all functions in the provider.

Here are a few useful links:

https://msdn.microsoft.com/en-us/library/6e9y4s5t.aspx

https://msdn.microsoft.com/en-us/library/2fx93s7w.aspx

https://msdn.microsoft.com/en-us/library/system.web.security.membershipprovider.aspx

http://stackoverflow.com/questions/22705072/umbraco-overriding-or-extending-default-membership-provider